We give an algebraic proof of the Pentagon Theorem. The proof works in all Miquelian Möbius planes obtained from a separable quadratic field extension. In particular, the theorem holds in every finite Miquelian plane. The arguments also reveal that the five concyclic points in the Pentagon Theorem are either pairwise distinct or identical to one single point. In addition we identify five additional quintuples of points in the pentagon configuration which are concyclic.
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 25 Ekim 2023 |
Yayımlanma Tarihi | 29 Ekim 2023 |
Kabul Tarihi | 27 Eylül 2023 |
Yayımlandığı Sayı | Yıl 2023 |